If $\cos(\alpha+\beta)=\large\frac{4}{5}$ and $\sin (\alpha-\beta)=\large\frac{5}{13}$ where $\alpha$ lies between $0$ and $\large\frac{\pi}{4}$,find the value of $\tan 2\alpha$

Question

$\begin{array}{1 1}(A)\;\large\frac{56}{33}&(B)\;\large\frac{55}{36}\\(C)\;\large\frac{53}{36}&(D)\;\large\frac{56}{23}\end{array} $